Can anyone fill in some gaps for me about them. Do the team have a rogues gallery? Do they have an arch-enemy? I also heard that the team died during their original series. Were they meant to stay dead? How many reboots have they had? I am interested in the team now, and I wouldn't mind getting some classic or pivotal issues. Thanks for the help.

Their primary arch enemies are the Brotherhood of Evil, led by the Brain and Monsieur Mallah.

Morrison sort-of revives them as the Brotherhood of Dada, and then the Brain and Monsieur Mallah show up in their own issue as a separate threat (if that's what you want to call it).

They were meant to stay dead.

They had been revived by Paul Kupperberg before this (he brought Larry and the Chief back from the dead and created Tempest), but that team fell apart too before this one was initiated.